Unformatted text preview: y giving a point on the curve, given by the two formulas above. However, since at these points ∂f ∂x ( ± 1 , 0) = ± 2 n = 0 , the theorem does guarantee a solution for x in terms of y ; in fact, near any point other than (0 , ± 1) (the “north pole” and “south pole”) we can write x = ψ ( y ), where ψ ( y ) = r 1 − y 2 for points on the right semicircle and ψ ( y ) = − r 1 − y 2 on the left semicircle....
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 Fall '08
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 Calculus, North Pole, South Pole, open arc

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